KS1 Reasoning & Problem Solving Questions · Reasoning and Problem Solving Questions ... March 2016 on Twitter in the run up to SATS. The answers are provided with some simple notes

KS1 Reasoning & Problem

Solving Questions

KS1

Reasoning and Problem Solving Questions

© Trinity Academy Halifax 2016

For information and comments email [email protected]

Information

This booklet contains over 40 reasoning and problem

solving questions suitable for KS1 classes. These are the

questions that we have been putting out each day in

March 2016 on Twitter in the run up to SATS.

The answers are provided with some simple notes at the

back of the booklet and for some questions

supplementary questions and variation has been

provided.

We hope to release more questions like this over the

course of next year including some open ended problems.

Please keep a look out for our work. If you have not seen

our schemes and assessments for primary then please

take a look at our website www.whiterosemathshub.co.uk

As always we welcome any feedback on the work we are

doing and the materials that we are releasing.

Thank you for taking an interest in our work.

The White Rose Maths Hub Team

mailto:[email protected]

http://www.whiterosemathshub.co.uk/

KS1




Children’s Reponses

Children’s responses will tell you a lot about their depth of

understanding of a given topic. For example

Children who reason verbally or written that 5 is less than 6

and then 24 is being added each time potentially indicate a

deeper understanding of number than those who work out

both sides of the inequality.

Bar Modelling – Pictorial Methods

Many of the problem solving questions in this booklet can

be solved using a bar modelling method. Encourage

children to use diagrams to help them solve the problem.

Here is a problem where bar modelling would help.

If you want to find out more about bar modelling please

contact the Hub.


Razza and Gina have the same number of stickers.

Razza gives 15 stickers away.

Gina gives 32 stickers away.

How many more stickers than Gina does Razza have now?

1 2

Stickers and Squares

Here is part of a number square.

5 6 7 8 9

15 16 17

25

Add together the two numbers that would be in the shaded squares.

Choose one of these symbols

<, > or =

to make the number sentences correct.

1 2

Calculations

24 + 5 24 + 6

18 + 3 17 + 4

33 + 15 40 + 8

Put the numbers 6, 7, 8, 9, 10 and 11 into the boxes.

Use each number only once.

23 + 10 + > 23 + 10 +

32 + + 5 < 32 + + 5

50 + 30 + = 49 + 29 +

Mary buys these two items.

She pays with the following coin.

Here is the change she is given.

Has she been given the correct change?

1 Presents

19 pence 2 Mo buys a key ring.

His mum gives him a quarter of the money.

How much money does he have to pay himself?

16 pence

16 pence

If

Work out

1

2 Number Problems

= 18

Here are some apples.

Class 2 are asked work out the total.

Here are four different ways they do it.

Fill in the missing blanks.

….. + ….. = 10

….. + ….. + ….. + ….. + ….. = 10

…… × …… = 10

…… × …… = 10

+ +

+ = 18

+

1

2

Number Problems

Here is a number line.

The number 14 is shown.

Mark the number 9 on the number line.

0

14

Here are some digit cards.

Meg and Sam each use two of the cards to make a number.

What is the difference between their two numbers?

I have I have made the largest number you can make.

I have made the smallest number you can make.

Erik bakes 5 trays of muffins.

Each tray contains 6 muffins.

He sells 16 muffins and eats 5

How many muffins does he have left?

1 2

Shopping and Baking

These items are sold in a shop.

Ray buys three items.

Two of them were the same item.

He spent £23

Which items does he buy?

Here is a blue strip of paper.

An orange strip of paper is four times as long.

The strips are joined end to end.

How long is the blue strip?

How long is the orange strip?

1 2

More Number Problems

Mike buys these items and it costs him 30 pence.

Olga buys these items and it costs her 42 pence.

How much does a ruler cost?

Find the cost of a ruler.

20cm

1

2

Problems Galore

Each purple block is 8cm long.

Each green block is 6cm long.

How long is a blue block?

Aron has some balloons.

Fiona has 12 more balloons than Aron.

In total they have 40 balloons.

How many balloons has Fiona got?

8cm

6cm

Here is a number puzzle.

The number in the middle is found by

Multiplying the two bottom corner numbers together

Then add on the top number

These three diagrams all have the same middle number.

1

Number Puzzles

2

2 2

5

9

2

8

7 4

4

8

5

Jeff is reading a book.

He reads 9 pages.

He has 3 pages left to read.

What fraction of the book does he have left to read?

Work out the missing numbers.

Sasha is playing a game to win prizes.

Each blue counter is worth 2 points.

Each green counter is worth 5 points.

She wins the following counters.

Which of these prizes can Sasha get?

1

Prizes and Balances

2 Here is a balance

Here is another balance

Work out the weight of two s.

50 points

25 points

30 points

40 points

18kg

72kg

1

Wednesday Workout

In the pyramids the two numbers below add to the make the number above.

Complete these two pyramids.

What is the value of the blue box?

How did you get your answer?

2

25

100 44

25

99 44

25

89

44

Marie is posting a letter and parcel.

It costs 29 pence to post the letter.

It costs 15 pence more to post the parcel.

Marie pays with this coin.

How much change does she get?

Class 2 are doing a survey.

They ask 20 children this question.

“How do you travel to school?”

Some results are shown in the pictogram.

The number of children who travel by car is half the number who walk to school.

Complete the pictogram.

Here is a toy car.

Here is a lolly.

How much longer is the lolly than the car?

1 Pictogram and Measures

2

Method of

travel Number of children

Walk

Car

Other

= 2 children

Sarah has some 10 pence and 5 pence coins.

She has five 10 pence coins.

Sarah has 85 pence in total.

How many 5 pence coins does she have?

Yasmin has 3 jars of bugs.

There are 7 more bugs in the first jar than the second.

There are 3 less bugs in the third jar than the second.

There are 40 bugs in total.

How many bugs are in the first jar?

1

Two wordy problems

2

For Q2 you might find it helpful to draw a bar model or other diagram.

Sam and Zoe are working out some subtractions.

Sam’s answer is double Zoe’s answer.

What could Zoe’s question be?

Mr Drake needs 20 metres of ribbon.

Red ribbon costs £5 per metre.

.

Green ribbon costs £2 per metre.

He buys 12 metres of red ribbon.

The rest is green.

How much does he spend in total?

1

Number Problems

2

I am working out 74 – 56

One of the numbers in my questions is 15

Sam

Zoe

Mika buys a bottle of water and a cheesecake.

He pays with the following coins.

He receives 18 pence change.

The water costs 29 pence.

How much does the cheesecake cost?

62 people are going to a football game.

They can travel in a bus or car.

A car can hold 5 people.

A bus can hold 15 people.

They plan to use 6 cars and 2 buses.

Can they all travel to the game?

1

Shopping and Football

2

Des has some oranges.

He packs them into boxes.

Each box holds 5 oranges.

He fills 7 boxes.

He has 29 oranges left.

How many oranges does he have in total?

1

Number Problems

2

Complete the number sentences.

5 + 5 + 5 + 5 + 5 + 5 = × 5

10 + 5 + 5 + 5 + 5 = × 5

10 + 10 + 2 + 2 = × 2

4 x 2 + 5 x 2 = × 2

Explain your methods.

Here are two number lines.

Find the difference between A and B.

1

Number Problems

2

In this diagram shapes represent numbers.

The sum of each row is shown at the side.

Find the value of each shape.

Here is a number sentence.

5 × > 32

What is the smallest whole number that can be used to make the sentence correct?

Here is another number sentence.

26 + 15 < 60 −

What is the greatest whole number that can be used to make the sentence correct?

1

Number Problems

3

2

Here is a number line.

Mark the number 1 on the line.

Here is a different number line.

Mark the number 1 on this line.

1

4

0

1

2

0

4

One egg and one slice of toast costs 74 pence.

One egg and two slices of toast costs £1

How much does an egg cost?

1

Breakfast Time 2

A TV show starts at this time.

The TV show lasts 45 minutes.

Maria looks at the clock during the show.

How many more minutes does the TV show last?

Emma has 87 Easter eggs.

She has some baskets to fill.

She fills each basket with 10 eggs.

How many baskets did she fill?

How many eggs did she have left?

If each basket held only 5 eggs, how would your answers change?

1

Number Problems

2

Joe has these coins.

Balloons cost 5 pence each.

He buys the following balloons.

How much money does he have left?

KS1




Sheet Answer Notes

Stickers and squares

17

76 Encourage students to try to answer the problem without filling in all the squares.

Calculations

<, =, = Encourage students to explain their reasoning without working out each individual calculation.

11, 10 7, 9 6, 8

Students should start with the last calculation. Various answers available.

Presents Yes With working

12 pence

Number problems

15

Square = 6 Circle = 9 To extend this students could make a calculation that adds up 24

5 + 5 2 + 2 + 2 + 2 + 2 2 x 5 5 x 2


KS1




Number problems

40

Shopping and baking Two chocolates and one teddy

Other questions you could ask: If you had £30 what could you buy?

9 muffins

More number problems 18 pence

Ask students how they can work out the cost of one pencil.

4 cm 16 cm

Split the strip into 5 equal parts

Problems galore 5 cm

Students may find it useful to mark on the diagram.

26 balloons A bar model diagram may help students answer this question.

Number puzzles

28 28, 10 0, 28

Can they find any more pyramids that make 28?

𝟏

𝟒


KS1




Prizes and balances Football or chew bar

54 kg Circle = 9 Square = 27

Wednesday workout

56, 13, 31 55, 14, 30 45, 24, 20

Can they see a pattern? What happens to the blue box when the number at the top changes?

27 pence

Pictogram and measures

3 circles for car 1 circle for other

4 cm longer

Two wordy problems 7

19 A bar model diagram may help students answer this question.

Number problems 15 – 6 or 24 – 15

£76 This is luxury ribbon!

Shopping and football 33 pence

No they will be two people short

With working.

Number problems 64 oranges

6 6

With explanations.


KS1




12 9

Number problems

13 A = 22 B = 35

Circle = 5 Triangle = 11 Trapezium = 9

Number problems

7

18

Other questions you could ask:

Where is 𝟏

𝟐 on the number line?

Other questions you could ask:

Where is 𝟏

𝟒 on the number line?

What is each marker worth?

Breakfast time

48 pence Students should work out what one slice of toast costs before working out the price of an egg.

10 minutes


KS1




Number problems

35 pence

8 baskets 7 eggs left 17 baskets 2 eggs left

Other questions you could ask: What if there were 93 eggs? What if each basket only held two eggs?


Documents

KS1 Reasoning & Problem Solving Questions · Reasoning and Problem Solving Questions ... March 2016 on Twitter in the run up to SATS. The answers are provided with some simple notes